2017/06/09 by Bitoun, Thomas
#Algebraic Geometry (math.AG) #FOS: Mathematics
paper · doi:10.48550/arxiv.1706.02843
Let D be the ring of Grothendieck differential operators of the ring R of polynomials in d≥3 variables with coefficients in a perfect field of positive characteristic p. We compute the D-module length of the first local cohomology module H1f(R) of R with respect to an irreducible polynomial f with an isolated singularity, for p large enough. The expression we give is in terms of the Frobenius action on the top coherent cohomology of the structure sheaf of the exceptional divisor of a resolution of the singularity. Our proof rests on a tight closure computation due to Hara. Since the above length is quite different from that of the corresponding local cohomology module in characteristic zero, we also consider a characteristic zero D-module whose length is expected to equal that above, for ordinary primes.